The Gold Market

Part 3

by J. Orlin Grabbe

Now that we have seen how spot gold is priced
"loco London," we can examine how other local markets,
and other types of gold contracts, are priced in
reference to the London spot market. This includes
other spot delivery locations, gold forward and futures
contracts--such as the gold futures contract at the
NYMEX in New York-- and gold swaps, forward rate
agreements, and options. (In 1994 the COMEX merged
with the NYMEX, and the principal gold futures contract
now trades there.)

London is only one of many important centers for
gold trading. The second principal center for spot or
physical gold trading, for example, is Zurich. For
eight hours a day, trading occurs simultaneously in
London and Zurich--with Zurich normally opening, and
closing, an hour earlier than London. During these
hours Zurich closely rivals London in its influence
over the spot price, because of the importance of the
three major Swiss banks--Credit Suisse, Swiss Bank
Corporation, and Union Bank of Switzerland--in the
physical gold market. Each of these banks has long
maintained its own refinery, often taking physical
delivery of gold and processing it for other regional
markets.

(On December 8, 1997, Swiss Bank Corporation and
Union Bank of Switzerland announced plans to merge, the
combined bank to be known as United Bank of
Switzerland. The net effect such a merger would
ultimately have on the Zurich gold market is not yet
clear.)

In addition to other gold delivery locations,
there are other weight and quality standards which
create differential prices. Examples include the
London and Tokyo kilobars (which are 32.148 ozs.,
instead of the circa 400 oz. "large bars"), the 10 tola
bars (3.75 ozs.) popular in India and the Middle East,
the 1, 5 and 10 tael bars (respectively 1.203, 6.017,
and 12.034 ozs.) found in Hong Kong and Taiwan, and the
baht bar (0.47 ozs) of Thailand. Gold content is
another difference. The London good delivery bar is
only required to have a minimum of 995 parts gold to
1000 parts total. But a gold content of 9,999 parts
gold to 10,000 parts total ("four nines") is commonly
traded, as is a content of 990 parts to 1,000 total
(the baht bar being an example of the latter ratio).
Gold purity is important to industry. Jewellers might
want gold in the form of grain for alloying, while
electronics firms may require "five nines"--meaning
.99999 purity.

Pricing Nonstandard Contracts

Nonstandard contracts can be priced by reference
to the standard loco London good delivery bar, by
taking into account the simple arbitrage relationships
that would turn one into another. The primary
variables to keep track of are the costs of shipping
gold from one location to another, the cost of refining
gold to different purity levels, and the interest or
financing cost for the time required to accomplish
these activities.

Suppose a dealer is offered non-good delivery bars
of .995 purity loco Panama City. Here is one chain of
calculations the dealer might go through to come up
with a price quotation. First the dealer notes that
London good delivery bars of .9999 purity can be sold
in Tokyo for $.50/oz premium to the standard loco
London price. He knows that if he buys the bars in
Panama, he could sell them in Tokyo, but first he would
have to ship them to an appropriate location to upgrade
their purity.

The dealer also knows that he can upgrade to
London large bars for good delivery, and have the gold
content refined to .9999 purity, for $.50/oz at the
Johnson Matthey refinery in Salt Lake City, Utah. There
is a two-week turnaround time for the upgrade.
Shipping time is one day from Panama City to Salt Lake,
and two days from Salt Lake to Tokyo.

The dealer calculates the cost of shipping and
insurance from Panama to Salt Lake as $.40/oz, while
shipping from Salt Lake to Tokyo is $.70/oz. The total
time consumed would be 15 days, which at 6 percent
interest and spot gold at, say, $300/oz amounts to 300
x .06 (15/360) = $.75/oz.

Therefore the dealer's best, or break-even,
quotation to the person offering him non-standard gold
bars in Panama City would be the spot price for good
delivery loco London minus $1.85. If spot gold were at
$300/oz. bid, the most the dealer could afford to bid
for the Panama bars would be $298.15/oz.

The Gold Lease or Gold Libor Rates

Gold bears interest. Positive interest. Many
people do not know this. They are used to the notion
of storing their gold with some bank or warehouse, and
paying for storage cost. They then view the storage
and insurance cost as a negative interest rate. But
this has little to do with the way gold is priced or
traded in the wholesale market.

The forward price of gold--the price agreed now
for gold to be purchased or sold at some time in the
future--is a function of the gold spot price, and the
interest rates representing alternative uses of
resources over the forward time period. So before we
discuss gold forward prices, we should discuss gold and
dollar interest rates.

This brings us to the gold lease rate, or the gold
interest rate paid on gold deposits. Another term that
is used is gold libor, by analogy with the London
Interbank Offered Rate for eurocurrencies traded in
London. Despite the apparent literal connotation of
each of these labels, "gold libor rates" and "gold
lease rates" are alternative descriptions that refer to
the bid-asked gold interest rates paid on gold. The
bid rate (deposit rate, borrowing rate) is the gold
interest rate paid for borrowing gold (that is, on gold
deposits), while the asked or offered rate is the gold
interest rate quoted for lending gold. The expressions
"bid-asked gold lease rates" or "bid-asked gold libor
rates" are thus interchangeable.

If the gold borrowing rate is 2 percent per
annum, for example, then 100 ozs of gold borrowed for
360 days must be repaid as 102 ozs of gold. (Gold
interest rates, like most money market rates, are
nearly always quoted on the basis of a 360-day year.)
In the early 1980s gold deposits rarely yielded over 1
percent, but in recent years have rarely yielded less
than 1 percent. The chart below, from Kitco, shows
gold lease rates from August 1993 to October 1996.
(More recent daily quotes can be found at the
Kitco web site.)

Because of large central bank gold holdings, gold
loans are one of the cheapest financing sources for the
gold mining industry. A mining company borrows gold
and sells it on the spot market to obtain funds for
gold production. The interest installments on the gold
loan are payable in gold. And when the loan matures,
the principal (and any final interest due) is repaid
directly from mine production.

Central banks are the major lenders of gold. They
accounted for around 75 percent of the gold on loan,
estimated at around 2,750 tonnes, at the end of 1996.
Central banks in recent years have been under pressure
to earn a return on their gold holdings, and therefore
lend to, for example, gold dealers who have mismatched
books between gold deposits and gold loans. (The
practice of central bank gold lending first became
newsworthy in 1990, when the investment banking firm
Drexel, Burnham, Lambert went bankrupt while owing
borrowed gold to the Central Bank of Portugal.)

The gold lending (or borrowing) rate, then, is one
of the components that determine the gold forward
price. Let's see how this works.

The Gold Forward Price

Suppose the spot price of gold is $300/oz. The
gold lease rate for 180 days is 2 percent per annum.
And the eurodollar rate for 180 days is 6 percent per
annum. (For simplicity here, we ignore all bid-asked
spreads. But they are easily included in the following
calculations.)

I borrow $300 at the eurodollar rate. In 180 days
I will have to repay the dollar borrowing with interest
in the amount $300 (1+.06(180/360)) = $300 (1.03) =
$309.

With the borrowed money I can buy 1 oz. of gold,
and place it on deposit for 180 days. The amount of
gold I will get back is 1 (1+.02(180/360) = 1 (1.01) =
1.01 oz.

Thus, 1 oz. of gold with a spot price of $300 has
grown into 1.01 ounces in 180 days, with a value of
$309. This translates into a 180-day forward value of
$309/1.01 = $305.94.

Spot price:

$300.00

180-day Forward Price:

$305.94

Notice that both the gold lease and the eurodollar rate
have gone into this calculation. Specifically:

$305.94 = $300 [1+.06 (180/360)] / [1+.02
(180/360)].

In general, if the spot price is S, the forward price
is F(T) for a time-horizon of T days (up to a year),
the eurodollar rate is r, and the gold lease rate is
r*, we have the relation

F(T) = S [1 + r (T/360)] / [1 + r* (T/360)].

Notice that in the numerical example we just used,
the forward price $305.94 is approximately 2 percent
higher than the spot price of $300. That is, the 180-
day forward premium of $5.94 is approximate 2 percent
of the spot price of $300. (An exact 2 percent would
be $6.) Why is this?

To see what is involved, let's subtract the spot
rate S from both sides of the above equation. The left-
hand side will be the forward premium F(T) - S.
Simplifying the right-hand side, we obtain:

F(T) - S = S [( r - r*)( T/360)] / [1 + r* (T/360)].

That is, the forward premium (F(T)-S) is approximately
equal to the spot rate S multiplied by the difference
between the eurdollar rate r and the gold lease rate r*
(once we have adjusted this rate for the fraction of a
year: T/360).

Since in the numerical example the eurodollar rate
was 6 percent, while the least rate was 2 percent, the
forward premium at an annual rate is approximately 6-2
= 4 percent. For 180 days, or half a year, it is
approximately 2 percent.

So, as long as we are talking about an annual rate-
-that is, before we do the days adjustment--the gold
forward premium in percentage terms is approximately
the difference between the eurodollar rate and the gold
lease rate.

We can view this same relationship in other ways:
given a eurodollar rate and a gold forward premium (in
percentage terms), we can back out the implied lease
rate.

Looking back at the chart from Kitco, above, it is
easy to see that subtracting the gold lease rate from
the "prime rate" gives us approximately the gold
forward rate. (Note that "prime rate" is a misleading
term to use: the relevant interest rate in the gold
market is the eurodollar rate by which banks borrow and
lend among themselves, not the commercial "prime"
lending rate--which is often an administered, rather
than a market, interest rate.)

Gold forward rates are sometimes referred to as
"GOFO" rates, because GOFO was the Reuters page that
showed gold forward rates.

Gold Swaps

There are many different hedging and trading
operations in the gold market, all of which bring us
back to the same relationship between forward and spot
rates we saw in the previous section.

For example, gold dealers will buy gold forward
from mining companies. The mining companies, thus
assured of a fixed forward price at which to sell their
production, go to work producing. Meanwhile, the gold
dealers, to hedge themselves against movements in the
gold price, borrow gold and sell it in the spot market.
(To repeat, dealers "borrow" gold by taking in gold
deposits, and paying out the gold lease rate.)

Restated, gold dealers buy gold forward from
mining companies at a price F(T). To hedge themselves,
the dealers borrow gold at an interest rate r*, and
sell it in the market at a price S. They earn interest
on the dollar proceeds of the spot gold sale at an
interest rate r.

Thus, for each ounce of gold purchased, the dealer
must pay

F(T) [1+ r* (T/360) ] .

While for each ounce of gold sold, the dealer earns:

S [1 + r (T/360)].

All excess profit (beyond bid-asked spread) gets
eliminated when these amounts are equal. Which gives

F(T) [1+ r* (T/360) ] = S [1 + r (T/360)] .

This is, of course, exactly the same formula as before.

Generally speaking, gold dealers will quote
forward prices to their customers (these are called
"outright" forwards), but forward trades beween dealers
mostly take place in connection with a simultaneous
spot transaction. That is, in the form of "swaps." A
swap transaction is a spot sale of gold combined with a
forward repurchase, or a spot purchase of gold combined
with a forward sale. This type of trading requires
less capital and is subject to less price risk. The
swap rate is F(T)-S, and as we saw before, this
difference is (when quoted as a percentage of the spot
price) essentially the difference between the
eurodollar rate and the gold lease rate.

A spot sale of gold combined with a forward
purchase is also called a cash-and-carry transaction.
The transaction provides immediate cash, the cost of
which is the carry, or the difference between forward
and spot rates. The dollar lender (who buys the gold),
meanwhile has possession of the gold as security. So a
cash-and-carry (one form of a swap) boils down to a
dollar loan collateralized with gold.

The typical dealing spread between eurodollar
deposits is 1/8 of 1 percent, or .125 percent, while
the typical spread between gold deposit and loan rates
is .20 percent. This translates into bid-asked swap
rate, or cash-and-carry, spreads of about .30 percent.
For example:

Eurodollar rates

Gold lease rates

Gold swap rates

1 month

3.0625-3.1875

0.50-0.70

2.35-2.65

3 months

3.1250-3.2500

0.55-0.75

2.40-2.70

6 months

3.3125-3.4375

0.70-0.90

2.45-2.75

12 months

3.5625-3.6875

1.00-1.20

2.35-2.65

Note that the gold swap rate can be independently
viewed as the collateralized borrowing rate. A small
central bank, for example, with plenty of gold to
spare, could borrow dollars for 3 months and pay--not
the 3-month asked eurodollar rate of 3.25 percent--but
rather the gold swap rate of 2.70 percent.